85.65.4 problem 5

Internal problem ID [22884]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. B Exercises at page 213
Problem number : 5
Date solved : Thursday, October 02, 2025 at 09:16:12 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (2 x +3\right )^{2} y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }-2 y&=24 x^{2} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 43

ode:=(2*x+3)^2*diff(diff(y(x),x),x)+(2*x+3)*diff(y(x),x)-2*y(x) = 24*x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (x +\frac {3}{2}\right ) c_2 +\frac {c_1}{\sqrt {x +\frac {3}{2}}}-12 \ln \left (2 x +3\right ) x +\frac {12 x^{2}}{5}-18 \ln \left (2 x +3\right )+\frac {46 x}{5}-\frac {93}{5} \]

✓ Mathematica. Time used: 0.076 (sec). Leaf size: 53

ode=(2*x+3)^2*D[y[x],{x,2}]+(2*x+3)*D[y[x],{x,1}]-2*y[x]==24*x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {2}{5} \left (6 x^2+38 x-15 (2 x+3) \log (2 x+3)-24\right )+c_1 (2 x+3)+\frac {c_2}{\sqrt {2 x+3}} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-24*x**2 + (2*x + 3)**2*Derivative(y(x), (x, 2)) + (2*x + 3)*Derivative(y(x), x) - 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-4*x**2*Derivative(y(x), (x, 2)) + 24*x**